Carol / Kynea Primes

[kar_bon]

(738^15864-1)^2-2 is prime, 90998 digits

pfgw64 -tp -q"(738^15864-1)^2-2"
PFGW Version 4.0.0.64BIT.20190528.Win_Dev [GWNUM 29.8]
Primality testing (738^15864-1)^2-2 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
(738^15864-1)^2-2 is prime! (534.4768s+0.1565s)

For this base there was no prime on the -1 side up to n=10k.
Primes so far, tested to n=25k:
-1: 15864
+1: 3, 18, 5892

No further reservation.

Stats: 82 bases < 3000 with no Carol prime.

[kar_bon]

Another one down:

Base 938 tested to n=22k
Found primes so far:
-1: 21852
+1: 54, 56, 654, 749, 3916, 11463
No further reservation.

(938^21852-1)^2-2 has 129898 digits

[Dylan14]

Base 832 complete to n = 25k. Seven primes found:

(832^26+1)^2-2
(832^51+1)^2-2
(832^62+1)^2-2
(832^5882+1)^2-2
(832^7795+1)^2-2
(832^8375+1)^2-2
(832^18830+1)^2-2

All but the last prime on the list was found by kar_bon, noted here: https://www.rieselprime.de/ziki/Carol-Kynea_prime_832

A Carol prime for this base remains elusive...

[kuratkull]

Base 42 tested to n=100k (continuing)
Two primes found:

(42^33475+1)^2-2 is 3-PRP! (135.6747s+0.0009s)
(42^40891-1)^2-2 is 3-PRP! (199.4855s+0.0010s)

[kar_bon]

Searched to n=52k and found:

PFGW Version 4.0.0.64BIT.20190528.Win_Dev [GWNUM 29.8]
Primality testing (832^51686-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 23, base 1+sqrt(23)
Running N+1 test using discriminant 23, base 2+sqrt(23)
(832^51686-1)^2-2 is prime! (13534.9333s+0.1916s)

301859 digits, so no Top5000 entry.

Another Carol-absence-base has fallen.

[gd_barnes]

Originally Posted by kar_bon

Searched to n=52k and found:

PFGW Version 4.0.0.64BIT.20190528.Win_Dev [GWNUM 29.8]
Primality testing (832^51686-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 23, base 1+sqrt(23)
Running N+1 test using discriminant 23, base 2+sqrt(23)
(832^51686-1)^2-2 is prime! (13534.9333s+0.1916s)

301859 digits, so no Top5000 entry.

Another Carol-absence-base has fallen.

Very good! I assume that you searched both Carol and Kynea to n=52k. I also assume that you are releasing this base. Is that correct?

[kar_bon]

As usual I always search both sides together and no further reservation on this base.

[rogue]

(1534^2147+1)^2-2
(1534^2665+1)^2-2
(1540^4484-1)^2-2
(1542^5825+1)^2-2
(1542^6888+1)^2-2
(1566^8188-1)^2-2
(1570^2310+1)^2-2
(1614^2907+1)^2-2
(1650^3219-1)^2-2
(1684^5605+1)^2-2
(1706^8028-1)^2-2
(1726^4221+1)^2-2
(1760^6210+1)^2-2
(1774^2061-1)^2-2
(1774^2249+1)^2-2
(1806^3666-1)^2-2
(1806^8128-1)^2-2
(1806^9942-1)^2-2
(1928^4650-1)^2-2
(1928^4870+1)^2-2
(1950^8442+1)^2-2
(1986^3738+1)^2-2
(2064^2698-1)^2-2
(2076^2217+1)^2-2
(2076^6182-1)^2-2
(2104^2741-1)^2-2
(2140^3857-1)^2-2
(2146^7710-1)^2-2
(2266^5906+1)^2-2
(2280^2590-1)^2-2
(2280^3443-1)^2-2
(2290^4114+1)^2-2
(2312^4671-1)^2-2
(2312^4887-1)^2-2
(2342^4232-1)^2-2
(2382^2498+1)^2-2
(2382^4175+1)^2-2
(2384^3411+1)^2-2
(2384^7398-1)^2-2
(2398^5485+1)^2-2
(2400^3148-1)^2-2
(2400^4589+1)^2-2
(2400^7021+1)^2-2
(2400^9993+1)^2-2
(2404^2828-1)^2-2
(2474^8041-1)^2-2
(2524^2208+1)^2-2
(2524^3272-1)^2-2
(2574^2280-1)^2-2
(2610^5581-1)^2-2
(2610^7874-1)^2-2
(2614^3383+1)^2-2
(2616^2457+1)^2-2
(2616^8123-1)^2-2
(2622^6882-1)^2-2
(2624^2702+1)^2-2
(2626^4436+1)^2-2
(2650^9393-1)^2-2
(2658^2548-1)^2-2
(2660^3979+1)^2-2
(2846^8189-1)^2-2
(2886^7330-1)^2-2
(2904^3400+1)^2-2
(2944^5817-1)^2-2
(2970^2993+1)^2-2

are all prime.